proof of Mollweide’s equations

We transform the equation




using the fact that γ=π-α-β. The left hand side can be further expanded, so that we get:


Collecting terms we get:


Using s:=a+b+c2 and using the equations

sinα2 = (s-b)(s-c)bc
cosβ2 = s(s-a)bc

we get:


which is obviously true. So we can prove the first equation by going backwards. The second equation can be proved in quite the same way.

Title proof of Mollweide’s equations
Canonical name ProofOfMollweidesEquations
Date of creation 2013-03-22 12:50:10
Last modified on 2013-03-22 12:50:10
Owner mathwizard (128)
Last modified by mathwizard (128)
Numerical id 5
Author mathwizard (128)
Entry type Proof
Classification msc 51-00